A "short sale" or "short payoff", in most cases will affect your credit, but it depends largely on how your lender will report the settlement to the credit bureaus. I am seeing "settled for less then full obligation" with increasing frequency and other professionals I speak with are reporting the same.
If your lender agrees to satisfy your mortgage in exchange for the net proceeds from the sale of your home and you agree to sign a new Note for less then remaining balance of your debt, then your lender is in fact forgiving a portion of your debt and will likely report the deal as "settled for less then full obligation".
When negotiating a short sale I always ask the lenders representative how the settlement will be reported to the credit bureaus. Very often the representative has no idea or furnishes misinformation, but I am finding that many lenders are including lanaguage in their final written short sale approval letter which spells out how the settlement will be reported to the credit bureaus.